The sexually-explicit saga from writer-director Lars von Trier is expected to do most of its business in the on-demand space, where it has been available since March 7. U.S. distributor Magnolia Pictures wasn’t talking numbers on the early business, other than to say that “it’s doing very well.”

While online downloads and VOD will provide the bulk of the returns, the box office is an unpredictable part of Magnolia’s plan for the film. “Nymphomaniac” will roll out in roughly 25 large-city U.S. theaters this weekend. It’s divided into two parts, and “Nymphomanic: Volume 2″ will be available on demand Thursday and open in theaters on April 4.

The limited theatrical/VOD approach can help smaller fare or challenging films like “Nymphomaniac” find an audience, as Roadside Attractions discovered with their 2012 release of the Richard Gere drama, “Arbitrage.” This release strategy is a natural for Magnolia; it’s the theatrical and home entertainment distribution arm of the Wagner/Cuban Companies, a group of media properties co-owned by Todd Wagner and Mark Cuban that also includes the Landmark Theatres chain and AXS TV.

“Volume 1″ follows a self-diagnosed sex addict (Charlotte Gainsbourg), who is discovered beaten in an alley by an older bachelor (Stellan Skarsgård). As he helps her recover from the trauma, she shares stories of her erotic exploits with a host of notables played by such actors as Shia LaBeouf and Jamie Bell.

LaBeouf, Christian Slater and Uma Thurman will all appear in part one, while part two will pick up with Bell, Willem Dafoe, Mia Goth and Jean-Marc Barr.

Magnolia submitted the sexually-graphic “Nymphomaniac” to the Motion Picture Association of America ratings board earlier this year, and — not surprisingly — it came back with an NC-17. Instead of submitting to the MPAA’s edit suggestions, Magnolia decided to release the film unrated.

“It’s not a huge distinction,” Magnolia’s sr. vice-president of marketing and publicity Matt Cowal told TheWrap. “But we went this route rather than accept the restrictions on promotions and marketing materials that an NC-17 would require.”

Last year, Sundance Selects faced a similar choice with Abdellatif Kechiche’s sexually explicit coming-of-age tale “Blue is the Warmest Color,” the Palme d’Or winner at the Cannes Film Festival. They opted to go with the NC-17 and it took in just over $2 million at the domestic box office.

In the last five years, more than 1,000 movies have been released without a rating, while only three have gone out with an NC-17. The most recent prior to”Blue is the Warmest Color” was William Friedkin’s “Killer Joe,” which grossed almost $2 million in 2012; the top-grossing was Steve McQueen’s “Shame,” which grossed $3.9 million in 2011.

As a rule, major exhibition chains like AMC Theaters and Regal Cinema don’t play movies that are available on demand. So while many exhibitors shy away from unrated fare, Magnolia will turn to independents and smaller chains for screens when it expands over the next few weeks. “We’ll have it in every major market eventually,” said Cowal.

“We’re not afraid of controversy,” said Thomas Ashley, chief executive at FlixFling, which is offering the film online.

“A lot of folks have been afraid of those films, saying that they were too extreme and that we shouldn’t release them but this is our business, whether a film is hard to watch or not. We like to release films the way the filmmaker intended.”

The critics have been impressed — it’s at 87 percent “fresh” on Rotten Tomatoes — but at this point no one expects “Nymphomaniac” to run up major grosses.

Von Trier is a giant in European cinema, but a niche taste for U.S. movie audiences. The director has a range of controversial and acclaimed films to his credit, including “Breaking the Waves,” “Dancer in the Dark” and “Dogville.” “Nymphomaniac” has taken in more than $9 million overseas for several local distributors, but his films have never found major commercial success in the U.S.

“Nymphomaniac” is the third film in von Trier’s “Depression Trilogy,” having been preceded by “Antichrist,” which took in less than a million dollars in 2009, and “Melancholia,” which grossed a solid $3 million for Magnolia in 2011.

The financial risk isn’t considerably high; “Nymphomaniac’s” budget was under $5 million, and Magnolia acquired U.S. rights from TrustNordisk in February for a reported $2 million.

“Maybe people will see ‘Volume 1′ in theaters and then watch the second part at home,” said Cowal.

Here’s a new trailer:

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